Question

Why is (1-x)^(-1/x)=e? I know that (1+x)^(1/x) is equal to e but I don’t understand with the negative there.

Answer 1

Briefly, it is because you left out `lim_(xrarr0)` and we know that `lim_(xrarr0)(-x) = lim_(xrarr0) (x)`

Explanation:

So

`lim_(xrarr0)(1-x)^(-1/x) = lim_(xrarr0) (1+(-x))^(1/(-x))`

`= lim_(xrarr0) (1+x)^(1/(x))=e`